Optimal Lot Size with Partial Backlogging Under the Occurrence of Imperfect Quality Items

Abstract

In this study, a continuous review inventory system with deterministic demand, partial backlogging, and imperfect quality items is considered. More precisely, the fraction of imperfect quality items is assumed as a random variable with a known distribution function. The order quantity is subjected to a 100%, error-free, screening process, with finite screening rate. After inspection, the imperfect quality items can be classified into two categories: low quality items and defective items. The demand rate is constant and manifests even during screening period. The demand during the stockout period is satisfied partially as soon as stock is available and before the new demand is met. Perfect and imperfect quality items are charged with different holding cost, giving the chance of different treatment for the two categories of products. The objective is to find the order quantity that maximizes the total profit of the system per unit time. Beyond, the analytical properties are established, the impact of imperfect quality and holding costs differentiation are examined and the behavior of the relative error using the EOQ with partial backlogging solution is displayed graphically. Finally, it is shown that this model can be reduced to other models existing in the literature.